Question

Apply the division algorithm to find the quotient and remainder on dividing f(x) by g(x) as given below:
$f\left(x\right)=x^4-3x^2+4x+5,g\left(x\right)=x^2+1-x$

• A. $Q=x^2-x-3$ , $R=8$
• B. $Q=x^2+x-3$ , $R=8$
• C. $Q=x^2+x+3$ , $R=8$
• D. $Q=x^2-x+3$ , $R=8$

Answer 1

Answer: (B)

$Q=x^2+x-3$ , $R=8$

Let us divide $f\left(x\right)=x^4-3x^2+4x+5$ by $g\left(x\right)=x^2+1-x$ as shown in the above image.

Hence, the quotient is $q\left(x\right)=x^2+x-3$ and the remainder is $r\left(x\right)=8$.